Summary: Vol. 11, No. 11/November 1994/J. Opt. Soc. Am. A 3069
Three-dimensional stereo by photometric ratios
Lawrence B. Wolff and Elli Angelopoulou
Computer Vision Laboratory, Department of Computer Science, The Johns Hopkins University,Baltimore, Maryland 21218
Received July 22, 1993; revised manuscript received March 9, 1994; accepted June 29, 1994
We present a novel robust methodology for corresponding a dense set of points on an object surface from
photometric values for three-dimensional stereo computation of depth. The methodology utilizes multiple
stereo pairs ofimages, with each stereo pair being taken of the identical scene but under different illumination.
With just two stereo pairs of images taken under two different illumination conditions, respectively, a stereo
pair of ratio images can be produced, one for the ratio of left-hand images and one for the ratio of right-
hand images. We demonstrate how the photometric ratios composing these images can be used for accurate
correspondence of objectpoints. Object points having the same photometric ratio with respect to two different
illumination conditions constitute a well-defined equivalence class of physical constraints defined by local
surface orientation relative to illumination conditions. We formally show that for diffuse reflection the
photometric ratio is invariant to varying camera characteristics, surface albedo, and viewpoint and that
therefore the same photometric ratio in both images of a stereo pair implies the same equivalence class
of physical constraints. The correspondence of photometric ratios along epipolar lines in a stereo pair of
images under different illumination conditions is therefore a robust correspondence of equivalent physical
constraints, and the determination of depth from stereo can be performed without explicit knowledge of
what these corresponding physical constraints actually are. Whereas illumination planning is required, our